Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Kant’s Mereological Account of Greater and Lesser Actual Infinities

Kant’s Mereological Account of Greater and Lesser Actual Infinities AbstractRecent work on Kant’s conception of space has largely put to rest the view that Kant is hostile to actual infinity. Far from limiting our cognition to quantities that are finite or merely potentially infinite, Kant characterizes the ground of all spatial representation as an actually infinite magnitude. I advance this reevaluation a step further by arguing that Kant judges some actual infinities to be greater than others: he claims, for instance, that an infinity of miles is strictly smaller than an infinity of earth-diameters. This inequality follows from Kant’s mereological conception of magnitudes (quanta): the part is (analytically) less than the whole, and an infinity of miles is equal to only a part of an infinity of earth-diameters. This inequality does not, however, imply that Kant’s infinities have transfinite and unequal sizes (quantitates). Because Kant’s conception of size (quantitas) is based on the Eudoxian theory of proportions, infinite magnitudes (quanta) cannot be assigned exact sizes. Infinite magnitudes are immeasurable, but some are greater than others. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Archiv für Geschichte der Philosophie de Gruyter

Kant’s Mereological Account of Greater and Lesser Actual Infinities

Smyth, Daniel
Archiv für Geschichte der Philosophie , Volume 105 (2): 34 – Jun 30, 2023
Download PDF
34 pages

Loading next page...
 
/lp/de-gruyter/kant-s-mereological-account-of-greater-and-lesser-actual-infinities-7OvyxjvJ0I

References

References for this paper are not available at this time. We will be adding them shortly, thank you for your patience.

Publisher
de Gruyter
Copyright
© 2021 Walter de Gruyter GmbH, Berlin/Boston
ISSN
0003-9101
eISSN
1613-0650
DOI
10.1515/agph-2018-0107
Publisher site
See Article on Publisher Site

Abstract

AbstractRecent work on Kant’s conception of space has largely put to rest the view that Kant is hostile to actual infinity. Far from limiting our cognition to quantities that are finite or merely potentially infinite, Kant characterizes the ground of all spatial representation as an actually infinite magnitude. I advance this reevaluation a step further by arguing that Kant judges some actual infinities to be greater than others: he claims, for instance, that an infinity of miles is strictly smaller than an infinity of earth-diameters. This inequality follows from Kant’s mereological conception of magnitudes (quanta): the part is (analytically) less than the whole, and an infinity of miles is equal to only a part of an infinity of earth-diameters. This inequality does not, however, imply that Kant’s infinities have transfinite and unequal sizes (quantitates). Because Kant’s conception of size (quantitas) is based on the Eudoxian theory of proportions, infinite magnitudes (quanta) cannot be assigned exact sizes. Infinite magnitudes are immeasurable, but some are greater than others.

Journal

Archiv für Geschichte der Philosophie – de Gruyter

Published: Jun 30, 2023

There are no references for this article.